#include <deal.II/base/polynomials_piecewise.h>

Inheritance diagram for Polynomials::PiecewisePolynomial< number >:

Public Member Functions
	PiecewisePolynomial (const Polynomial< number > &coefficients_on_interval, const unsigned int n_intervals, const unsigned int interval, const bool spans_next_interval)

number	value (const number x) const

void	value (const number x, std::vector< number > &values) const

void	value (const number x, const unsigned int n_derivatives, number *values) const

unsigned int	degree () const

template<class Archive >
void	serialize (Archive &ar, const unsigned int version)

virtual std::size_t	memory_consumption () const

Protected Attributes
Polynomial< number >	polynomial

unsigned int	n_intervals

unsigned int	interval

bool	spans_two_intervals

Subscriptor functionality
Classes derived from Subscriptor provide a facility to subscribe to this object. This is mostly used by the SmartPointer class.
void	subscribe (std::atomic< bool > *const validity, const std::string &identifier="") const

void	unsubscribe (std::atomic< bool > *const validity, const std::string &identifier="") const

unsigned int	n_subscriptions () const

template<typename StreamType >
void	list_subscribers (StreamType &stream) const

void	list_subscribers () const

using	map_value_type = decltype(counter_map)::value_type

using	map_iterator = decltype(counter_map)::iterator

std::atomic< unsigned int >	counter

std::map< std::string, unsigned int >	counter_map

std::vector< std::atomic< bool > * >	validity_pointers

const std::type_info *	object_info

static std::mutex	mutex

static ::ExceptionBase &	ExcInUse (int arg1, std::string arg2, std::string arg3)

static ::ExceptionBase &	ExcNoSubscriber (std::string arg1, std::string arg2)

void	check_no_subscribers () const noexcept

Detailed Description

template<typename number>
class Polynomials::PiecewisePolynomial< number >

Definition of piecewise 1D polynomials for the unit interval. This space allows the description of interpolating polynomials on parts of the unit interval, similarly to the definition of finite element basis functions on subdivided elements. The primary purpose of this class is to allow constructing the shape functions of the FE_Q_iso_Q1 class that has a number of interpolation points in each coordinate direction, but instead of using them for higher-order polynomials just chooses piecewise linear shape functions – in effect, it is a \(Q_1\) element defined on a subdivision of the reference cell, and replicated on each of these sub-cells.

This class is not derived from the ScalarPolynomialsBase base class because it is not actually a polynomial – it is a piecewise polynomial. However, it is interface-compatible with the Polynomials::Polynomial class, and consequently can be used as template argument for TensorProductPolynomials.

Definition at line 64 of file polynomials_piecewise.h.

Constructor & Destructor Documentation

◆ PiecewisePolynomial()

template<typename number >

Polynomials::PiecewisePolynomial< number >::PiecewisePolynomial	(	const Polynomial< number > &	coefficients_on_interval,
		const unsigned int	n_intervals,
		const unsigned int	interval,
		const bool	spans_next_interval
	)

Constructor for Lagrange polynomial on an interval that is a subset of the unit interval. It uses a polynomial description that is scaled to the size of the subinterval compared to the unit interval, the total number of intervals (subdivisions), the current index of the interval as well as if the polynomial spans onto the next interval (e.g., if it lives on two neighboring intervals).

If the number of intervals is one, the piecewise polynomial behaves exactly like a usual polynomial.

Definition at line 27 of file polynomials_piecewise.cc.

Member Function Documentation

◆ value() [1/3]

template<typename number >

number Polynomials::PiecewisePolynomial< number >::value ( const number x ) const

inline

Return the value of this polynomial at the given point, evaluating the underlying polynomial. The polynomial evaluates to zero when outside of the given interval (and possible the next one to the right when it spans over that range).

Definition at line 209 of file polynomials_piecewise.h.

◆ value() [2/3]

template<typename number >

void Polynomials::PiecewisePolynomial< number >::value	(	const number	x,
		std::vector< number > &	values
	)		const

Return the values and the derivatives of the Polynomial at point x. values[i], i=0,...,values.size()-1 includes the ith derivative. The number of derivatives to be computed is thus determined by the size of the vector passed.

Note that all the derivatives evaluate to zero at the border between intervals (assuming exact arithmetic) in the interior of the unit interval, as there is no unique gradient value in that case for a piecewise polynomial. This is not always desired (e.g., when evaluating jumps of gradients on the element boundary), but it is the user's responsibility to avoid evaluation at these points when it does not make sense.

Definition at line 45 of file polynomials_piecewise.cc.

◆ value() [3/3]

template<typename number >

void Polynomials::PiecewisePolynomial< number >::value	(	const number	x,
		const unsigned int	n_derivatives,
		number *	values
	)		const

Return the values and the derivatives of the Polynomial at point x. values[i], i=0,...,n_derivatives includes the ith derivative.The number of derivatives to be computed is determined by n_derivatives and values has to provide sufficient space for n_derivatives + 1 values.

Note that all the derivatives evaluate to zero at the border between intervals (assuming exact arithmetic) in the interior of the unit interval, as there is no unique gradient value in that case for a piecewise polynomial. This is not always desired (e.g., when evaluating jumps of gradients on the element boundary), but it is the user's responsibility to avoid evaluation at these points when it does not make sense.

Definition at line 57 of file polynomials_piecewise.cc.

◆ degree()

template<typename number >

unsigned int Polynomials::PiecewisePolynomial< number >::degree

inline

Degree of the polynomial. This is the degree of the underlying base polynomial.

Definition at line 200 of file polynomials_piecewise.h.

◆ serialize()

template<typename number >

template<class Archive >

void Polynomials::PiecewisePolynomial< number >::serialize	(	Archive &	ar,
		const unsigned int	version
	)

inline

Write or read the data of this object to or from a stream for the purpose of serialization using the BOOST serialization library.

Definition at line 251 of file polynomials_piecewise.h.

◆ memory_consumption()

template<typename number >

std::size_t Polynomials::PiecewisePolynomial< number >::memory_consumption

virtual

Return an estimate (in bytes) for the memory consumption of this object.

Definition at line 123 of file polynomials_piecewise.cc.

Member Data Documentation

◆ polynomial

template<typename number >

Polynomial<number> Polynomials::PiecewisePolynomial< number >::polynomial

protected

Underlying polynomial object that is scaled to a subinterval and concatenated accordingly.

Definition at line 156 of file polynomials_piecewise.h.

◆ n_intervals

template<typename number >

unsigned int Polynomials::PiecewisePolynomial< number >::n_intervals

protected

A variable storing the number of intervals that the unit interval is divided into.

Definition at line 162 of file polynomials_piecewise.h.

◆ interval

template<typename number >

unsigned int Polynomials::PiecewisePolynomial< number >::interval

protected

A variable storing the index of the current polynomial in the range of intervals.

Definition at line 168 of file polynomials_piecewise.h.

◆ spans_two_intervals

template<typename number >

bool Polynomials::PiecewisePolynomial< number >::spans_two_intervals

protected

Store if the polynomial spans over two adjacent intervals, i.e., the one given in subinterval and the next one.

Definition at line 174 of file polynomials_piecewise.h.

The documentation for this class was generated from the following files:

include/deal.II/base/polynomials_piecewise.h
source/base/polynomials_piecewise.cc

Public Member Functions

Protected Attributes

Subscriptor functionality

Detailed Description

Constructor & Destructor Documentation

◆ PiecewisePolynomial()

Member Function Documentation

◆ value() [1/3]

◆ value() [2/3]

◆ value() [3/3]

◆ degree()

◆ serialize()

◆ memory_consumption()

Member Data Documentation

◆ polynomial

◆ n_intervals

◆ interval

◆ spans_two_intervals